Problem: Simplify the following expression: $r = \dfrac{50q + 80}{40q - 40}$ You can assume $q \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $50q + 80 = (2\cdot5\cdot5 \cdot q) + (2\cdot2\cdot2\cdot2\cdot5)$ The denominator can be factored: $40q - 40 = (2\cdot2\cdot2\cdot5 \cdot q) - (2\cdot2\cdot2\cdot5)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $r = \dfrac{(10)(5q + 8)}{(10)(4q - 4)}$ Dividing both the numerator and denominator by $10$ gives: $r = \dfrac{5q + 8}{4q - 4}$